The scene where Mrs. Brisby gives Timmy his medicine while the song "Flying Dreams Lullaby" plays in the background, and the other Brisby children watch, wondering if their brother is going to be okay.
The harshest part of this scene is the fact that Never Say "Die" is averted by children. The children crowd around Timothy's bed, clearly worried, and ask their mother if he's going to die.
Cynthia: Is Timmy gonna die?
Mrs. Brisby: No, sweetheart. He's just very sick.
Theresa: What's the matter with him, Mother?
Mrs. Brisby: Mr. Ages called it...pneumonia.
Cynthia: When will he get better?
Mrs. Brisby: Soon...I hope.
And later, when using the power of the amulet previously given to her by Nicodemus, Mrs. Brisby single-handedly moves her home to safety.
The part after the home was completely submerged in the mud is exceptionally well handled, at least in terms of Mrs. Brisby' reaction. She has a very disturbed (and disturbing) wide-eyed expression, summarizing the horror and shock of a widow seeing her house with all her children and her best friend sink while the rescuers are just standing next to it, unable to do anything against it. Plus, they forcefully drag her away from said sinking house while she watches, being all hysterical and quite possibly near breakdown. It is only moments later that there is any indication that this predicament would be resolved.
If that wasn't bad enough, they show the children terrified, scrambling for survival.
The part when Mrs. Brisby finds out what happened to her husband always made me very sad, as a kid. As well as disturbed me.
It's that little hitch in her voice as she's reading from Nicodemus's journal that gets the tears flowing:
Mrs. Brisby:[reading] "He was ki.." [her voice breaks] "...killed today....while drugging the farmer's cat, Dragon." Oh, I....I never knew...just what happened.
It's also a nasty bit of Fridge Horror when you realize Mrs. Brisby hadn't known until then just how her husband died. It's likely he just never came home one night and she was forced to assume the worst. If she had never visited the rats, it's likely she never would have gotten closure for what happened to Johnathan.
This is actually explicitly stated in the original novel.
Hell, pretty much any time she's forced to remember her late husband or invoke his name for help there's a little catch in her voice. The wound is still very fresh.
Nicodemus's opening monologue as he laments Johnathan's death and wonders what will happen to his wife now:
Nicodemus: Jonathan was a dear friend. I am lost, knowing how to help his widow. She knows nothing of us, or the Plan. Perhaps best that I do nothing at present. I shall miss him. Jonathan, wherever you are, your thoughts must comfort her tonight. She'll be waiting, and you will not return. Farewell...my friend.
The death of Nicodemus as well as Justin and Mr. Ages's reactions to it.
Justin has a momentary Heroic BSOD, while Mr. Ages breaks down and seems to start crying as he tells Mrs. Brisby what happened. Ages has been rather crotchety in all his previous scenes, but his sorrow makes sense when you realize that he and Nicodemus escaped NIMH together and must have been very old friends.
You have to feel sorry for Jeremy near the end, after going through all sorts of hell to impress Mrs Brisby, he finally comes back enthusiastically with string in tow to lift her house out of the mud, only to realize he's missed the whole ordeal. Dejected he fails to see any other point for the string anymore ("What's a guy like me gonna do with a love nest anyway?") and slowly walks away slumped over. However, just then a klutzy female crow crashes into him...